BBC RD 1995/1

Research andDevelopment

Report

MODULAR ACOUSTIC DIFFUSER:The development and performance of a

modular acoustic diffuser

R. Walker, B.Sc.(Eng), C.Eng., F.I.O.A., M.I.E.E. and M.D.M. Baird, M.I.E.T.

Research and Development DepartmentTechnical Resources Division

THE BRITISH BROADCASTING CORPORATION

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MODULAR ACOUSTIC DIFFUSER:The development and performance of a modular acoustic diffuser

R. Walker, B.Sc.(Eng), C.Eng., F.I.O.A., M.I.E.E. and M.D.M. Baird, M.I.E.T.

Summary

The development of a prototype modular acoustic diffuser into a commercially reproducibleproduct is described. The difficulties with materials, manufacturing processes and withfire-safety considerations are discussed. Acoustic measurements carried out on the finalproduction modules showed that the diffuser met the acoustic requirements, despitesimplifications and departures from the theoretical construction. In near-field conditionstypical of installations in small studios and control rooms, the reflection characteristics departsignificantly from the predictions of the far-field theory.

Issued under the Authority of

BBC RD 1995/1

Research & Development Department,Technical Resources DivisionBRITISH BROADCASTING CORPORATION

General ManagerResearch & Development Department

British Broadcasting Corporation

No part of this publication may be reproduced, stored in aretrieval system, or transmitted in any form or by anymeans, electronic, mechanical, photocopying, recording,or otherwise, without prior permission.

(R008) 1995

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MODULAR ACOUSTIC DIFFUSER:The development and performance of a modular acoustic diffuser

R. Walker, B.Sc.(Eng), C.Eng., F.I.O.A., M.I.E.E. and M.D.M. Baird, M.I.E.T.

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2. ACOUSTIC BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

3. PROTOTYPE CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

4. ALTERNATIVE CONSTRUCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

4.1 Vacuum forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

4.2 Moulded plaster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4.3 Casting using foam materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4.4 Casting using filled materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4.5 Commercial moulding using self-skinning plastic foam . . . . . . . . . . . . . . . . . . . . . 3

4.6 Timber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4.7 Fabrication using metal or wood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4.8 Glass-reinforced plastic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

5. PERFORMANCE TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

5.1 Absorption coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

5.2 Directional response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

6. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

7. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

MODULAR ACOUSTIC DIFFUSERS:The development and performance of a modular acoustic diffuser

R. Walker, B.Sc.(Eng), C.Eng., F.I.O.A., M.I.E.E. and M.D.M. Baird, M.I.E.T.

1. INTRODUCTION

The use of special acoustic diffusing elements in thedesign of many types of room is commonplace. Someform of deliberate acoustic diffusion has beenincorporated into studios virtually since the beginningof broadcasting. More recently, structures based onnumber theory have been developed1. These overcomemany of the defects inherent in simple geometricdiffusing shapes and have achieved wide acceptance instudios, control rooms and public performancespaces2– 5.

In order to assist in the control of one particular type ofacoustic problem, the BBC developed a type ofacoustic diffuser which did not then exist in acommercial form6.

Tests on this modular diffuser, and an experimentalinstallation, showed that it dramatically reduced theproblem for which it had been specially designed. Itwas also generally applicable, especially as itconformed to the standard dimensions of the mostcommon kind of modular acoustic treatment, and to thedimensions of standard suspended ceiling structures (atleast, metric ones).

The construction of the prototype diffusers wasexpensive (at least, it was thought to be so at the time)and the resulting diffuser was relatively unattractiveand heavy. However, all of the original tests and theexperimental installation were done using thosehand-assembled, prototype modules. In addition, itlater became evident that the experimental modules didnot have a very long service lifetime. In the testinstallation, over a period of about three years, themodules eventually began to fall to pieces, because ofcreep in the adhesive. Despite this, the users of the areacontaining the experimental installation were reluctantto permit its removal until a replacement batch ofdiffusers had become available.

2. ACOUSTIC BACKGROUND

The theoretical background to the design of diffusingelements based on number theory is given in Refs. 1

and 3. In brief, such a diffuser consists of a one- ortwo-dimensional array of rectangular open ‘wells’ ofdiffering depths. The depths are arranged so thatphases of the reflections from their top surfaces (that is,after the sound wavefront has travelled from the top ofthe well to the bottom and back again) form aninterference pattern, as though from an irregulardiffraction grating. By appropriate design, it is possibleto create diffraction patterns corresponding to (nearly)uniform reflection; that is, creating an approximationto Lambertian reflection in either two or threedimensions, depending on the type of diffuser.

The background and theoretical basis of the BBCdesign is given in Ref. 6. The numerical basis of thatparticular design resulted not in a uniform reflectionpattern but in a selective cancellation of the reflectedenergy in the specular direction, at some frequencies.The otherwise uniform reflection pattern contained anull in the direction where a flat plate would have hadits maximum response. This module was primarilyintended to diffuse the mid-frequency sound energywhich otherwise gets trapped between ceiling and floorsurfaces in many studios and control rooms*. In theBBC-design, the side-walls of the wells were omitted.This modification greatly simplified the construction,without significantly affecting the acousticperformance, at least for normal-incidence sound.

The final design of the modular diffuser consistedessentially of a 12 × 12 array of square-section prismsof different heights, arranged adjacent to each other.The cell size was nominally 47.5 mm square and theheights ranged up to 200 mm. Fig. 1(overleaf)shows thegeneral appearance. The overall dimensions of themodule were 594 × 594 mm, to fit into standard600 mm-centre suspended ceiling grids.

3. PROTOTYPE CONSTRUCTION

The prototype diffusers were made from square-sectionrigid polyvinyl chloride (pvc) tube of about 2 mm wallthickness. This material was not available as a standardproduct with a section of 47.5 mm. Instead, forthe prototypes, the nearest stock size of 45 mm squarewas used. This resulted in an overall size of 540 mm

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* The problem frequently arises when the wall surfaces of a room are very heavily treated with acoustic absorption, in order to obtain low values of reverberationtime. It is not generally feasible to treat the floor and ceiling surfaces with so much acoustic absorption; the usual carpet- and ceiling-tile finishes providehigh-frequency absorption only. The result is a lack of absorption between about 500 Hz and 2000 Hz, for sound travelling between floor and ceiling. Having anull in the direction normal to the diffuser surface assists in the attenuation and scattering of that energy.

square and left a 20 mm border all round. The end-capswere also available as standard items. They weremoulded in high-density polyethylene. Sections oftube, cut to the correct lengths, were assembled by handon a plywood base. The base was machine slotted tolocate the tube sections. The tube sections were gluedin position, both to each other and to the baseboard.Fig. 2 shows the final appearance of the prototypediffuser. The total weight was about 10 kg. An estimateof about £35 was made for the unit cost of theseprototype modules.

A set of 16 of these prototypes was constructed for usein measurements and tests. An experimentalinstallation in the Television Music Studio Annexeproved to be entirely satisfactory, at least acoustically.

4. ALTERNATIVE CONSTRUCTIONS

At the time, it was felt that the hand-assembledmodules were unsatisfactory. They were rather heavierthan the target weight of about 5 – 6 kg, set by theload-bearing properties of typical suspended ceilingstructures. (This was not, of course, a significantproblem for wall-mounting.) They were also fairlyunattractive because of the narrow gaps between thetubes and the general fabricated appearance. It was alsothought at the time that the unit cost was too high.

The main problem with the prototype modules was thelack of fire-resistance of the material. Plastics such aspvc emit large quantities of dangerous fumes in fires.Plastics like polyethylene frequently assist the spreadof fires by melting and falling onto other combustiblematerials, especially when used in ceilings. The use ofrelatively large numbers of modules, each consisting ofabout 10 kg of such materials in the ceilings of

technical areas was completely unacceptable, as along-term proposition.

It was thought that some form of moulding or castingtechnique could produce one-piece units in quantity, ata reasonable cost. One of the difficulties with any formof moulding process was extracting the finisheddiffuser from the mould. The 200 mm deep by 47 mmwide, straight-sided, rectangular-section elementsmade extraction difficult, whatever the mouldingprocess. The shape was such that either expansion orcontraction during hardening would cause some part ofthe diffuser to grip the mould. In most tests of mouldingprocesses, the rectangular section elements had to bemodified to include a release (or ‘draw’) angle.

4.1 Vacuum forming

The first idea for mass production of cheap and lightmodules was the vacuum-forming of a relatively thinplastic sheet. As a fire-hazard, the small quantity ofmaterial involved should have been acceptable, even ifthe material itself was not especially fire-resistant.Similar materials and constructions are used widelyand in significant quantities, even in technical areas, inthe form of lighting diffusers.

Two problems arose to prevent the use of that methodof manufacture. The first was the difficulty ofmoulding the deep and narrow profile of the diffuser.That problem might have proved insurmountable, hadthe principle been pursued. The main, andover-whelming, obstacle was the non-acceptance ofthose types of material by the (BBC) fire safetymanagers. This was despite the fact that substantialamounts of similar materials are, usually, alreadypresent in the form of light fittings. It was found that, intechnical areas and along escape routes, the maximum

Fig. 1 - General appearance of diffuser. Fig. 2 - Final appearance of prototype diffuser.

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permissible quantities of such materials are limited toabout those that already exist in the form of lightfittings.

A vacuum-formed version of the diffuser, with amaximum depth of 50 mm rather than 200 mm, wassuccessfully developed. This has been used in someareas for experimental purposes. Because of its limiteddepth, it had a restricted performance at lowfrequencies. Fig. 3 shows a photograph of one of thesemouldings.

4.2 Moulded plaster

In principle, moulded hard plaster would form an idealconstruction material. It is an intrinsically cheapmaterial which is in common use and is capable ofproviding a high-quality surface finish.

In practice, it requires reinforcement to ensure adequatestrength. It is heavy and would require an advancedmoulding technique to achieve the thin sectionsnecessary to achieve reasonably low finished weight.

Some experiments were carried out by a commercialplaster-moulder, one who specialised in architecturalmouldings. Again, because of the deep sections, thediffuser had to be hand-layed. The final weight, about20 kg, was excessive and the manufacturing time taken,and the consequent cost, was also excessive.

Some discussions were held with another specialistplaster moulder*, who had developed a high-pressuremoulding technique. This was already being applied toa similar acoustic product, although of significantlyless complexity. The standard of production was highand the unit marginal costs very low indeed. However,the investment required to produce a suitable mouldwas considered to be excessive. Ultimately, a modulesimilar enough to the BBC design to be considered as areplacement was produced commercially by thecompany**.

4.3 Casting using foam materials

The two great difficulties with any moulding techniqueproducing thin-walled sections are the requirement for(and consequent expense of) a two-part mould, and thedifficulties with material flow in the narrow internalspaces. With materials like reinforced plaster or filledpolymers, the mould-closing forces necessary for the600 mm square diffuser would have been measured inhundreds of tonnes. The mould has to withstand thoseforces without serious distortion. This can only be

achieved by heavy, metal moulds, with their attendanthigh manufacturing costs.

As an alternative, it was thought that a solid castdiffuser might be acceptable, if the material densitycould be made low enough. The mould volume wasabout 45 litres, requiring a finished density of about150 kg/m3 for a reasonable final weight.

Some types of plastic foam material will expand oncuring to produce a lightweight foam with a solidsurface skin.

Tests on these materials showed that a satisfactory skinwas not produced unless the material was cured underclosely-controlled conditions, in a pre-heated mould.The material characteristics were unpleasant duringfoam production and curing. The cured polyurethanematerial was also not acceptable to the fire authorities.

4.4 Casting using filled materials

Some moulding tests were carried out using inherentlynon-flammable materials; for example, vermiculitefiller with a cement binder. Although the final densityachieved was reasonably acceptable, the strength andsurface finish were not adequate.

4.5 Commercial moulding using self-skinning plastic foam

Discussions were held with a commercial moulder ofinjection-moulded, self-skinning polyurethene foam.Samples of high quality mouldings were examined andestimates obtained for the preparation of a mould. Inthe event, the costs were too high. The polyurethene

Fig. 3 - Vacuum-formed, shallow diffuser.

* Acoustic GRG Products of Smarden, UK.

** On behalf of RPG Diffusor Systems Inc., of Upper Marlboro USA.

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material was also unacceptable to the fire authorities.

4.6 Timber

Some early prototypes were made of solid timbersections. These were visually attractive, but weighedabout 45 kg. They were thought to be too expensive toproduce and far too heavy for most applications.

Many commercial acoustic diffusers are made fromsolid timber or timber-based materials. They sufferfrom the same drawbacks.

4.7 Fabrication using metal or wood

Many possibilities for the fabrication of the diffusersfrom metal or wooden components were considered. Inone realisation, a combination of metal strips folded toform the front surface and one set of side walls andpre-cut metal sheets to form the other side-walls of thecells could be used. They were to be joined by gluing orsoldering.

Apart from models, no complete test of any of thesemethods was carried out. It was thought to be toodifficult to produce a visually acceptable product,without excessive finishing processes. The manufac-turing labour costs would also be high, even before theaddition of the finishing-process costs.

The module strength, however, would have beenexcellent and the total weight very low. If made entirelyof metal, they would also have been completelynon-flammable.

4.8 Glass-reinforced plastic

The only process tested that produced an acceptablesurface finish at a reasonable weight and withrelatively low mould manufacturing costs was the useof glass-reinforced polyester resin. To enable themodule to be extracted from the mould, a 11⁄2° drawangle was necessary. Significant force also had to beused — to the extent that the back surface had toinclude special reinforcement to withstand the loads. Inorder to achieve a reasonable degree of fire-resistance,it was necessary to use a relatively thick fire-retardantgel coat. The construction process was essentiallymanual. The gel coat, reinforcement fibre and polyesterresin were hand layed, in a one-part mould.

The final wall thickness was about 2 mm. The surfacefinish was excellent, although minor airholes usuallyhad to be filled by hand. It could be obtained as aself-coloured finish or spray-painted afterwards. Thestrength was, if anything, excessive for the application,but thinner wall sections could not be achieved reliably.

At about 7.5 kg, the module was somewhat heavierthan the target weight, but acceptable for mostpurposes. At about £140, the final production cost wasalso much greater than had been hoped for.

Although the materials used were described as being“reduced flammability” (Class 1 to BS476, Part 7 andClass 0 to Section E15 of the 1976 BuildingRegulations), the BBC fire safety managers had somereservations about their use. The insurance safetyexperts insisted on the addition of a fire-resistant sheet(6 mm vermiculite), which had to be permanently fixedin the back of the module. A fire-test was commis-sioned at a commercial Laboratory (SGS YarsleyTechnical Centre, Redhill). This showed that thediffuser did not compromise the fire-integrity of astandard false ceiling. It remained entirely solid,though significantly charred, when subjected to the testfire load of 105 kWhr (a peak thermal load estimated atabout 1 MW). It also emitted some additional smokefumes during the test, compared with a standard ceilingtile.

This development of the modular diffuser wascontinued to the point at which commercial productioncould be undertaken. Fig. 4 shows a photograph of afinished production module.

5. PERFORMANCE TESTS

The experimental installation in the Television Musicstudio had shown that significant beneficial effectswere achieved in practice, even with a very low densityof installation (less than 20% in that case).

Objective measurements were carried out when thefirst batch of production modules became available.The measurements had been delayed until that pointbecause the form of the production modules wassignificantly different to any of the developmentalconstructions.

5.1 Absorption coefficient

For a device whose main function was the reflection ofsound energy, it was necessary for the intrinsicabsorption to be reasonably small.

A standard ISO absorption coefficient test was carriedout on a set of 25 modules, arranged in a singlecontiguous patch. The sample was spacedapproximately 300 mm above the floor surface,supported on the normal ceiling-tile test frame. Thiswas intended to simulate their use in a suspendedceiling. The results were calculated, using as a basis,the plan area of the sample. They are shown in Fig. 5.

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At most frequencies, the absorption coefficient wasabout 0.3 at low frequencies, falling to 0.1 at higherfrequencies. This is somewhat higher than was hoped,but was not unreasonable. The modules have an actualsurface area of approximately four times their planarea. Based on that area, the intrinsic surface absorptioncoefficients lay in the range 0.075 to 0.025. Thesevalues were as expected for such materials. Someexcess absorption may have arisen from the supportingstructure and the panels used to enclose the sides of thesample — at such low values of absorption manynormally insignificant factors become important.

The absorption coefficient characteristic contains threeor four anomalous peaks. The one at 80 Hz, whichreaches an absorption coefficient of 0.7, was probablydue to the mounting conditions and resonances of thesample as a whole (or of individual complete modules)on the suspension system. It would probably not occurin a normal suspended ceiling system, because it wouldbe supported much more frequently by stiff tensionmembers rather than the rather flexible beams of thetest arrangement.

The second and third absorption peaks, at 630 Hz and1250 Hz, reaching 0.35 and 0.25 respectively, arealmost certainly due to the obscure excess absorptionmechanism described in Ref. 7. In that reference, amechanism for excess absorption is described whichdepends on resonance interactions between adjacentcells in the diffuser. The mechanism involves largevolume airflows from one cell into a neighbouring cellat certain mutual resonance frequencies. Because theairflow is forced to travel over the sharp edge of the celldivider, the path is very restricted and the normal airviscosity loss (which is practically insignificant in

unconfined flows) becomes dominant. Absorptioncoefficient peaks up to 0.8 – 1.0 are predicted. Thesimplified BBC diffuser has no cell dividers, but it isprobable that some residue of the effect is present. Thepeak effective absorption coefficients of about 0.35and 0.25 are not unduly problematical, although theyare higher than would be ideal.

The fourth absorption peak, at 6300 Hz, is small: itmay have been a measurement uncertainty or it mayhave been due to mechanical resonances of particularparts of the diffuser. For example, all of the square topsurfaces of the ‘blocks’ making up the diffuser areabout the same size as each other and have similar edgemounting conditions. It is possible that these very stiffand quite light panels could all resonate at 6300 Hz. Ineither case, the effect is small enough to be negligiblefor practical purposes.

5.2 Directional response

The measurement of directionality of a reflectingsurface is non-trivial. The immediate question to beasked is: “how far away from the reflector should thesource and receiver be?”. All of the theory, both for theBBC design and for others, is for the far-field response;that is, at distances for both source and receiver wherethe wavefronts are plane and the size of the objectinsignificant. This is a theoretical ideal which isdifficult to approach in development and testing andwhich almost never applies in practice, especially insmall rooms*.

Ref. 8 describes measurement techniques whichinvolve source-sample and receiver-sample distancesof about 9.1 m and 4.6 m respectively. The samplesizes

0

0.

0.

0.

0.

0.

0.

0.

0.

0.

1.

abso

rptio

nco

effic

ient

63 5 0 0 1000 2000 4000 80001/3 octave band centre frequency, Hz

Fig 5 - Absorption coefficient of final production diffuser.Fig. 4 - Final production diffuser.

* The special case of repeated floor-ceiling reflections, which the BBC diffuser was specially designed to counter, approaches the far-field condition because ofthe repetition. In the later part of the sound decay where this problem becomes evident, say after about 0.2 s, the sound may have travelled about 65 m; that ismore than 20 double reflections. Without additional diffusion, the wavefornts are then likely to be practically plane.

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were either 0.6 × 2.4 m or 1.2 × 2.4 m, depending onthe type of measurement. These are not strictly far-fielddimensions, although they are reasonablyrepresentative of some types of installations, especiallyin large performance spaces. Ref. 8 also includes somecomparisons between the measured directivities of aflat sheet and the theoretical responses. The agreementsare very close, showing that the methods of bothcalculation and measurement are valid.

Fig. 6 shows three calculated responses, as an exampleof the differences in effective response which can becaused by variations of source and receiver distances. Itshows the spatial response of a flat sheet, 2.4 m square,as the angle between the receiver position and thenormal is changed. In the orthogonal direction, thesource, the normal to the sheet, and receiver areco-planar. In Fig. 6(a) the source is located on thenormal to the sheet, at a distance of 9.1 m. The receiverdistance is 4.6 m. The frequency is 564 Hz. Theseconditions correspond to those of Fig. 23 in Ref. 8, forthe wavelength “λ = D/4 = 24" ”. Apart fromdeviations caused by the differences in angularsampling intervals (and probably differences in theresolution of the numerical summations of waveletcontributions) the results are identical. Fig. 6(b) showsthe calculated response for the same conditions exceptwith source and receiver distances that are 10 timeslarger. The characteristic, regular lobe structure is nowclearly evident. This is close to the theoretical far-fieldspatial response, as normally calculated for manyacoustic examples. The source and receiver distancesinvolved, namely 91 m and 46 m respectively, arerarely encountered in interior acoustic designs.

Fig. 6(c) shows the calculated response for a sourcedistance of 2.8 m and a receiver distance of 2.0 m.These distances are representative of those encounteredin normal control rooms and small studios. Clearly, thepattern of reflection is very different, with littleevidence of the pronounced lobe structure. Thesedistances are also the ones used for the measurementsdescribed in this Report.

In carrying out measurements of directionality, somemeans must be found to eliminate other reflections (forexample, from the surfaces of the test room) and toseparate the signals representing the incident andreflected sound waves. The latter co-exist in the samespace, although potentially at different times. Thegeometry of the measuring arrangement and theinstrumentation used must be capable of distinguishingbetween them. It is not practicable, in ordinaryroom-acoustic work, to make the distinction by otherphysical means, such as highly directional sources

and/or receivers, as might be done in radio-frequencyor ultra-sonic measurements.

The effects of the room boundaries might beminimised by making the room very large or using anexterior measurement field. Alternatively, by makingthe room surfaces very absorbent, as in an anechoicchamber, the effects of reflections from the roomsurfaces can be reduced. The use of time-domainwindow techniques9 to separate the incident andreflected sound can also assist in the rejection ofreflections from the room boundaries. Othermeasurement techniques for separating the incidentand reflected sound based on acoustic holography (thatis measurement and processing of the combinedfield10 – 12), might also be employed. These also requirethe use of an anechoic room.

Despite the foregoing limitations, an anechoic chamberwas used for the measurement of the reflectioncharacteristics of the BBC modular diffusers. This waspartly because a suitable large open space was notavailable. However, as measurements at very shortdistances, typical of control room and small studioinstallations, were required, this was not a seriousdisadvantage.

One of the difficulties with relying on absorption tocontrol the effects of reflections from the measurementroom was the large area of boundary surface incomparison with a typical test sample. Even in ahigh-quality anechoic chamber13, the sum of theresidual reflections from the whole of the interiorsurface can be significant in comparison with thewanted reflection from a practical-sized test sample.This was to form a slight, but significant, limitation tothe measurements.

Fig. 7 (see page 8)shows the geometry of the testarrangement. With this arrangement it was possible toachieve a time-domain discrimination between incidentand reflected sound of about 10 ms for all receiverangles between 0° and+50° and for source angles of 0°and −30°. With a half-Hanning window9, 14 a fre-quency resolution of about 150 Hz could be obtained.

Measurements of reflection amplitudes were made* fora 2 × 2 array of diffuser modules (total size 1.2 ×1.2 m) with source angles of 0° and−30° for steps ofreceiver angle from 0° to 50° in 2° steps. An identicalset of measurements was also carried out for a flatsheet of the same overall size. Measurements wereconfined to a plane normal to the test sample. All of theresults have been equalised to the direct response of theloudspeaker, as measured in the room without the test

* The measurements and data processing were carried out by J. Rabone.

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Fig. 6 - Calculated flat sheet responses.

(a) As Ref. 8

(b) ‘far-field’

(c) ‘near-field’

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object present, and in the position which would havecorresponded to the geometric image of themicrophone had the test object been present. Thiscompensated for the (slightly) irregular frequencyresponse of the loudspeaker and the overall path lossdue to the loudspeaker-microphone distance. It did notcompensate for the additional variation in response ofthe loudspeaker with radiation angle. These wereassumed to be small over the range of angles used.

The measured data required extensive post-processingin order to make them suitable for existing computerpresentation programs. After much experimentation, astandard mathematical processing package(Mathematica ®) was used to generate contour plots ofsound level as a function of direction and frequency.This required an interpolation function to be applied tothe data arrays in order to obtain logarithmic frequencyspacing for presentation in the usual form for audioacoustic results.

Many forms of presentation of the results are possible.The three-dimensional nature of the results ideallyrequired a three-dimension presentation. Any otherpresentation (for example, polar plots of directionalityfor a small sample of frequencies or frequency responseplots at particular angles) are so selective as to bevirtually useless. Three-dimensional presentations inthe form of contour plots do, at least, contain all of thedata. All of the results presented in this Report are inthat form.

The general background interference from the walls ofthe anechoic room limited the measurable range ofreflected sound to about 20 dB. At some angles andfrequencies, the measurable range approached 10 dB.Thus, the range of the results was limited to 20 dB atmost frequencies and angles and 10 dB at someparticular combinations of angle and frequency. Thisespecially affected the depths of the measured minimain the responses. These might otherwise have beenrather deeper than they appear. This does notsignificantly affect the overall appearance of the resultsnor the conclusions derived from them.

Fig. 8 shows the directivity response obtained from thediffuser array with normal incidence sound. Thisshould be compared with Fig. 9 which shows theresults of the same measurement for a flat plate. Thediffuser clearly disrupts the regular sidelobe rippleresponse of the flat plate. At most angles andfrequencies, no significant structures are visible in theresults for the diffuser array. At low frequencies (300 –400 Hz) and possibly at very high frequencies(8 – 10 kHz) there is some evidence of specularreflection from the diffuser array outside its designoperating frequency range of 688 – 3600 Hz. (The

horizontal streaks visible in Fig. 8 at about 20°, 30° and40° are measurement artifacts and should be ignored.)There is very little evidence in Fig. 8 of the theoretical(far-field) response nulls at 688 Hz and harmonicsthereof. In principle, the response for either a diffuseror a flat plate for normally-incident sound should besymmetrical about the normal. Figs. 8 and 9 thereforeonly show one half of the total hemispherical reflectionresponse.

Thus, the effective working frequency range of thediffuser, for normal incidence, extends upwards fromabout 600 Hz.

Fig. 10 (see page 10) shows the diffuser response forsound that is incident at –30° relative to the normal.Fig. 11(see page 11)shows the corresponding responseof the flat plate. For the diffuser, the response is shownfor angles between−50° and 50° because, theoretically, itshould be uniform over the whole hemisphere, at leastin the far-field. The flat plate response clearly showsthe low-frequency specular response, although thespecular angle appears to be about 24° rather than 30°.(This may have been due to cumulative errors in themeasurement of angles. The error is not important tothe main argument.) Fig. 11 also shows thesymmetrical side-lobe ripple response.

The spatial response of the diffuser for sound incidentat −30° is complicated. At frequencies below the designlower limit of 668 Hz there is a clear specular reflectionat about 20 – 30°, the apparent direction of which isslightly frequency dependent. The general appearancecompares quite closely with that for the flat plate in the

diffuser array withmounting pole

microphoneat 50°

source at -30°

sourceon axis

microphoneat -50°

Fig. 7 - Geometry of test arrangement in anechic room.

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Fig. 8 - Response of diffusers for normal incidence.

Fig. 9 - Response of flat plate, for normal incidence.

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same frequency and angle ranges. In the non-specularquandrant, the levels are significantly lower. Theseresults show that, as expected, the diffuser arraybehaves in a similar way to a flat sheet at frequenciesbelow its design lower limit.

At higher frequencies, the diffuser array again shows areasonably uniform reflection pattern. It is especiallynotable that the typical reflection amplitudes in thenon-specular quadrant are similar to those in thespecular quadrant, showing that the reflection offrequencies within the normal working range is nearlyomni-directional (in the reflection half-space). There isno significant evidence of pronounced structures in thereflection response in either quadrant. Again, there isvery little evidence of the theoretical nulls in the

response at 688 Hz and harmonics.

At frequencies above the design upper limit of about3600 Hz, the array clearly still behaves as a diffuser, aswould any highly irregular surface. At these higherfrequencies, there is some evidence that the diffusertends to reflect more sound energy in the non-speculardirection than in the specular direction, that is, backtowards the source rather than away from it. This is notvery surprising — without the cell wall dividers, thediffuser has a large exposed surface area to soundincident from the side. It therefore behaves as aneffective and reasonably omni-directional diffuser,even above its design frequency range. To some degree,this behaviour was anticipated, but the uniformity ofthe high-frequency response was a unexpected bonus.

Fig. 10 - Response of diffuser array for –30° incidence.

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Thus, the effective working frequency range of thediffuser at oblique angles of incidence extends upwardsfrom about 800 – 900 Hz.

6. CONCLUSIONS

The development of a modular acoustic diffuser fromthe original, hand-built prototype has been a difficultand complicated job. Most of the difficulties arose fromthe complex shape, especially the deep and narrowrecesses. The final design is much more expensive thanhad been hoped. However, it compares moderately wellwith other similar products.

The satisfying of various fire authorities and fire-safetyregulations also presented severe difficulties andseriously limited the range of usable materials.

Acoustic tests carried out on the final version of thediffuser have shown it to have reasonably lowabsorption characteristics.

The reflection characteristics have been shown to bemuch as expected, although the theoretical predictionswere based on the far-field theory. In the near-fieldconditions typical of most such diffuser installations,the module has a useful frequency range from about600 Hz upwards for normally-incident sound and about

800 – 900 Hz for oblique-incident sound. At very highfrequencies, the module behaves as an effective,near-random diffuser, even though the (far-field)frequency range is theoretically limited to about3600 Hz.

7. REFERENCES

1. SCHROEDER, M.R., 1975. Diffuse soundreflection by maximum-length sequences.J. Acoust. Soc. Am., 57 , January, pp. 149-150,

2. SCHROEDER, M.R., 1984. Progress inarchitectural acoustics and artificial reverberation:Concert hall acoustics and number theory.J.A.E.S., 32(4), April, pp. 194-203

3. D’ANTONIO, P. and KONNERT, J.H., 1984.The reflection phase grating diffusor: designtheory and application.J.A.E.S., 32(4), pp. 228-236.

4. D’ANTONIO, P. and KONNERT, J.H., 1984.The RFZ/RPG approach to control roommonitoring. 76th Audio Engr. Soc. Convention,New York, October, preprint #2157.

5. MARSHAL, A.H. and HYDE, J.R., 1982. Theacoustical design of Wellington Town Hall:design origins, research reviews and acoustical

Fig. 11 - Response of flat plate, –30°incidence.

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objectives.Proc. Inst. Acoustics,Edinburgh.

6. WALKER, R., 1990. The design andapplication of modular acoustic diffusingelements. BBC Research Department ReportNo. RD 1990/15.

7. KUTTRUF, H., 1994. Sound absorption byPseudostocastic diffusers (Schroeder diffusers).Applied Acoustics,42, pp. 215-231.

8. D’ANTONIO, P. and KONNERT, J.H., 1992.The directional scattering coefficient: experi-mental determination. J.A.E.S., 40(12),pp. 997-1017.

9. WALKER, R., 1995. Controlled image design:the measurement of time-frequency responses.BBC Research & Development Report No.RD 1995/3

10. ANDO, Y., 1968. The interference patternmethod of measuring the complex reflectioncoefficient of acoustical materials at obliqueincidence. Trans. Inst. Electron. Commun.Eng.Jpn.,51A, pp. 303-310.

11. TACHIBANA, H., YANO, H. and ISHII, K.,1978. Oblique incidence sound absorptioncharacteristics of various absorbing materialsmeasured by cross-correlation methods.J. Acoust. Soc. Am.,Jpn. (E) ,34, pp. 11-20.

12. TAMURA, M., 1990. Spatial Fourier Transformmethod of measuring reflection coefficients atoblique incidence I: Theory and numericalexamples.J. Acoust. Soc. Am., 88, pp. 2259-2264.

13. GILFORD, C.L.S., SHORTER, D.E.L.,HARWOOD, H.D., CHEW, J.R., DEANE, R.L.,1965. Design of a new free-field soundmeasurement room: specification and per-formance. BBC Research Department ReportNo. 1965/17.

14. HARRIS, F.J., 1978. On the use of windows forharmonic analysis with the discrete FourierTransform. Proc. I.E.E.E., 66(1), January,pp. 51-84.

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Published by BBC RESEARCH & DEVELOPMENT DEPARTMENT, Kingswood Warren, Tadworth, Surrey, KT20 6NP